Thick, elliptical-planform fin for a water sports board

ABSTRACT

A thick, elliptical-planform fin for use on a water sport board such as a surfboard. One set of attributes of the fins according to the present invention is the use of a substantially thick cross-section which, at its maximum thickness, overhangs the receiver slot, typically a 12 to 15 percent thickness ratio, with a maximum thickness at 30 percent of chord length, a blunter leading edge, and a short elliptical planform of constant relative dimension cross-section along its length.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority from U.S. Provisional PatentApplication No. 61/071,152 filed Apr. 15, 2008 entitled A Thick,Elliptical-Planform Fin for a Water Sports Board.

FIELD OF THE INVENTION

This invention relates to the field of water sports boards such assurfboards and in particular to an improved design of fin for suchboards.

BACKGROUND OF THE INVENTION

Surfing is a popular sport, enjoyed throughout many parts of the worldtoday. Surfing generally involves a surfer riding a wave while uprighton a surfboard. The surfer controls the surfboard by positioning himselfat different locations on the surfboard and by varying his center ofgravity. The surfboard (and other types of water sport boards) typicallyhas one or more fins, located on the underside of the surfboard thathelp direct the flow of water and have a substantial effect on thestability and the maneuverability of the surfboard.

The initial goal was to make longboards, surfboards longer than 9 feetin length, more maneuverable and turn better. Due to their largerdisplacement, longboards paddle faster and are better able to catchsmaller waves than shorter surfboards. However due to their longerlengths and heavier weight, longboards don't turn or manoeuvre as wellas shorter surfboards. The intent was to improve the performance ofsurfboards, specifically long boards, by applying aerodynamic theory toincrease the performance of the surfboard fins.

Surfboards originally did not have a fin. Originally surfboards wereheavy long planks of wood that had no fin. A surfer dragged his foot inthe water to turn the surfboard.

In the 1950's the construction of surfboards changed with theintroduction of foam core construction and the incorporation of a largekeel-like fin at the tail of the surfboard. The fin helped the boardtrack straight. The intent to riding was to drop into a wave, controlthe stall rate to set up for the tube ride, and drive the boardstraight. There was no maneuvering such as seen today.

Modern surf fins have been patterned after the planform shape of finsfound on fish. These fins allowed development of a new style of surfingthat involved considerable maneuvering. These smaller fins, coupled withsmaller boards gave birth to the style of surfing people are accustomedto today. The planform was cut to match a desired shape and the leadingand trailing edges were ground by hand.

In the early 1970's multi fin arrangements started to emerge. Twin finsetups were the first to gain market dominance. The twin fin setup hasremovable fins that were spaced apart on opposite sides of the rear ofthe board and each fin could be adjusted in its receiver box that wasmounted in the board. A male tang protruding from the base or root ofthe fin mated into a female slot in the receiver box. Because ofvariations found in the depth of the slots between different types ofreceiver boxes, and because fins were often fashioned from plate-likematerial, such as of fibreglass, having a thickness of less than orequal to ⅜ inch and then hand ground into the desired platform andthickness profile, the thickness of a fin was kept to no more than thewidth of the slot opening. This allowed the fin root to be pushed intothe slot if the tang was otherwise too short to properly seat againstthe base, i.e. bottom, of the slot.

A three fin “thruster” setup emerged in the early 1980's and has beendominant in the short board market until today. Typically the outermostfins have flat inner surfaces with curved outer surfaces. Additionallythe fins toe slightly inward pointing toward the nose of the board.During maneuvering, when the surfer shifts his weight toward the rear ofthe board, the flow off the tail of the surfboard tends to be moreradial, meaning that the outermost fins are experiencing positive anglesof attack. When the surfer shifts his weight forward so the surfboardrides flatter in the water for speed, the flow tends to come morestraight off the tail of the board, meaning that the toed-in outer finsare experiencing negative angles of attack. The sharp leading edge andthin thickness ratio of conventional fins encourages flow separationaround the fin and noticeable drag. A variation on the thruster setup isthe 2+1 setup, with two smaller outer fins and a larger central fin,this arrangement is common on longboards. The fins typically stillretain the rearwardly raked planform shape mimicking fish fins.

Typically the chord length of such conventional fins, where the finrakes back, is longer that the chord length of the base of the fin. Thefin is thinner at the tip than at the base. While the base is typically8% thick, towards the tip of the fin where the chord is longer and thefin thinner, the fin may be only 5% thick. Most longboard fins start asa ⅜ inch thick piece of fibreglass that is cut to the desired planformprofile and shaped by hand using a grinder.

The resulting cross section of popular longboard cutaway style fins areoften unintentionally non-symmetrical about their center line, have aflat middle section that extends to roughly 60% of chord length, andhave a sharp leading edge. Most fin manufacturers focus on the planformshape with almost no emphasis or analysis of the cross-sectional shape.This is especially the case with longboard fins.

The most common fin shape for outside fins for Thruster and 2+1 setupsare flat on inside surface and have a large flat section through most ofthe middle of upper surface of the fin, and have a sharp leading edge.During aggressive maneuvering the fins are subject to alternatingpositive and negative angles of attack. The sharp leading edges and flatbottom surfaces of the fin encourage separation of low angles of attackand an increase in the resultant drag.

Surfboard fins with thin cross-sections (typically 6 to 8% inthickness), sharp leading edges, surfaces that have abrupt changes inthe radius of curvature (referred to as curve incontinuity), and finswhere the thickest part of the fin is located more rearward (40 to 50%of chord length), are common designs found throughout the surfingindustry today.

It is an object of the present invention to provide fins for watersports boards which are more responsive, cause less drag, and enable thesurfboard to run faster in the water than conventional fins.

SUMMARY OF THE INVENTION

The thick, elliptical-planform fin apparatus described herein is for useon a water sport board such as a surfboard. The fin provides forimproved stability and maneuverability for the water sport board. Thefin has a tang portion which attaches the base or root of the fin to thewater sport board to transfer the forces of the fin to the board. Thefin has a hydrodynamic portion that extends into the water thatinteracts and directs the flow of water to provide stability andsteering for the water sport board. The tang attaches to a receivermounted into the water sports board such that the fin is removable. Anyof several different conventional styles of tang can be used which arecompatible with receivers commonly found in water sports boards. One setof attributes of the fins according to the present invention is the useof a substantially thick cross-section which, at its maximum overhangsthe receiver slot, typically 12 to 15 percent thickness ratio as seen inFIG. 1, with a maximum thickness at 30 percent of chord length, ablunter leading edge, and a short elliptical planform of constantrelative dimension cross-section along its length. These attributescombine to provide substantial hydrodynamic benefit when compared withavailable surfboard fins on the market today.

The present invention may be characterized as a surfboard fin formounting into a slot in a receiver box in the underside of a surfboard,where the fin includes:

-   -   an elliptical planform having a root and an opposite tip, said        root and said tip separated by a longitudinally extending length        defining a height of the fin, a leading edge and an opposite        trailing edge extending from said root to said tip along        opposite edge of said planform,    -   said planform having a thickness defined by cross-sections of        said planform, wherein said cross sections are substantially        orthogonal to said length, and extend along corresponding chords        of said cross sections between said opposite edges so as to        extend from said leading edge to said trailing edge, a ratio of        said thickness and said chord of each of said cross sections        defining a corresponding thickness-to-chord ratio,    -   and wherein substantially all of said thickness-to-chord ratios        are substantially equal to one another, and are greater than        substantially a thickness-to-chord ratio of twelve,    -   and wherein a ratio of a square of said longitudinally extending        length and a planform area of said planform define a        corresponding aspect ratio, and wherein said aspect ratio is        less than three,    -   and wherein said each of said cross sections has a nose section        at a forward end thereof corresponding to said leading edge, a        curved mid section including a maximum thickness position, and a        tapered rear section corresponding to said trailing edge, and        wherein said nose section, mid section and rear section of said        each of said cross sections is defined by a curvature which is        substantially that of a non-cambered NACA four digit airfoil        shape so as to have a substantially parabolic nose section and a        continuously smoothly substantially convexly curved mid section,        where said nose section, said mid section and said rear section        form a single smoothly continuously curved foil section which is        symmetric on opposites sides of said chord, and wherein said        maximum thickness position is located substantially at 30        percent of said chord on said each of said cross sections,    -   and wherein said length has a linear slope component relative to        said root chosen from forward slope, no slope, rearward slope,        and wherein said length has an elliptical sweep component        relative to said root chosen from forward sweep, no sweep,        rearward sweep,    -   and wherein irrespective of said sweep said planform is        substantially elliptical and its corresponding lift distribution        is also substantially elliptical and has a surface area which is        substantially constant for a particular said aspect ratio and        for particular said cross section and corresponding said        thickness-to-chord ratio and corresponding said maximum        thickness position,    -   and wherein said planform does not have winglets or auxiliary        foils protruding therefrom.        -   The fin may further include a tang depending from said root,            wherein a maximum root thickness, defined as said thickness            of said root at said maximum thickness position, is greater            than a width of the opening in the slot of the receiver box            so as to overhang said root from the slot when said tang is            mounted in the slot.        -   The maximum root thickness may be in the range of            substantially one half inch to one inch for use with a            receiver box having slot width of less than three eighths of            an inch. The maximum root thickness may be substantially            three quarters of an inch.        -   The linear slope component and said elliptical sweep            component may be applied to a substantially 30 percent chord            line corresponding to said maximum thickness positions. The            slope is forward and said sweep may forward or rearward.        -   The slope may be rearward and said sweep is forward or            rearward.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention can be further understood by reference to thefollowing description and attached drawings that illustrate aspects ofthe invention. Other features and advantages will be apparent from thefollowing detailed description of the invention, taken in conjunctionwith the accompanying drawings, which illustrate, by way of example, theprinciples of the present invention. In the drawings like characters ofreference denote corresponding parts in each view.

FIG. 1 is a prior art fin, viewed in planform, and mounted onto the tailend of a surfboard.

FIG. 2 illustrates one fin cross-section according to the presentinvention, normalized from 0 to 1.

FIG. 3 illustrates an example of a planform view of the fin according tothe present invention with tang suitable for mounting in 10.5 finreceiver box.

FIG. 3 a illustrates perspective view of a fin according to the presentinvention showing its constant cross-section symmetrical shape extendingfrom the fin root to the tip of the fin.

FIGS. 4 a and 4 b illustrate an example planform view of the finaccording to the present invention with tangs suitable for mounting inother types of receivers commonly found on water sport boards.

FIG. 5 illustrates an underneath view of a longboard showing typical finplacement and using fins according to the present invention.

FIG. 6 a illustrates an elliptical planform having no slope or sweep.

FIG. 6 b illustrates an elliptical planform having no linear slopecomponent and a forward elliptical sweep component.

FIG. 6 c illustrates an elliptical planform having a rearward linearslope component and forward elliptical sweep component.

FIG. 6 d illustrates an elliptical planform having a rearward linearslope component and a rearward elliptical sweep component.

FIG. 7 is a plot of planform area of a fin according to one embodimentof the present invention

FIG. 8 is a plot of a chord slope, linear component of the fin of FIG.7.

FIG. 9 is a plot of a chord slope, elliptical component for theembodiment of FIG. 8.

FIG. 10 is a plot of the fin profile for the embodiment of FIG. 8.

FIGS. 11 a and 11 b, 12 a and 12 b, 13 a and 13 b are plots of the chordslope elliptical component and fin profile respectively for threefurther embodiments of the fin according to the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

The present invention relates in general to a fin apparatus and methodof making same, where the fin is for use on a water sport board such asa surfboard, and, more particularly, relates to a thick, short or lowaspect ratio elliptical planform fin having substantially thickcross-section (typically 12-15% thickness ratio) which overhangs thereceiver box slot, and having a maximum thickness position at 30% ofchord length, and a blunter leading edge.

In the following description of the invention, reference is made to theaccompanying drawings, which form a part thereof, and in which is shownby way of illustration a specific example whereby the invention may bepracticed. It is to be understood that other embodiments may be utilizedand structural changes may be made without departing from the scope ofthe present invention. The thick, elliptical planform fin structure andmethod described herein is designed to operate on a water sport board.

FIG. 1 illustrates a prior art fin. FIG. 2 illustrates an example crosssection of fin 10 according to the present invention normalized from 0to 1. Fin 10 provides a reaction force when in motion relative to thesurrounding water. FIG. 2 illustrates a symmetrical foil shape with a15% thickness ratio. The shape is symmetrical about the center line with0% camber, or no arching of the shape. The shape has a 15% thickness tochord length ratio, or it is 15% as thick as it is long. The chord isthe imaginary straight line through the cross-section that connects theleading edge to the trailing edge. The maximum thickness of the examplefin is located at 30% of chord length, the leading edge is rounded andblunt, the trailing edge comes to a sharp point, and the upper and lowersurface form a smooth curve with no “flat spots” or abrupt changes incurve continuity.

FIG. 3 illustrates a planform view of an example longboard center finaccording to the present invention suitable for mounting in a surfingindustry standard 10.5 inch fin receiver box 22. The fin 10 has aleading edge 12 (0% of chord length), a trailing edge 14 (100% of chordlength), a fin tip 16, and a fin root 18 that is attached to the fintang 20 which is removably securable into a fin receiver box 22.Receiver box 22 is permanently mounted into a surfboard 24 as seen inFIG. 5. The height dimension 24 (also referred to herein as the length)of the fin 10 is measured as seen in FIG. 3 perpendicularly from theroot 18 to the tip 16. The vertically extending lines 26 represent linesof constant chord percentage. The chord percentage is the ratio of thedistance from the leading edge 12 to a given point (at a constant finheight), to that point's associated chord length. Surfboard fin 10 usesa constant relative dimension cross-sectional shape such as seen in FIG.2 applied along the entire height of the fin.

FIG. 3 a illustrates a tilted perspective view of the thick,elliptical-planform fin without tang or mounting base, to show thesymmetrical shape from FIG. 2 extending from root 18 to tip 16.

FIGS. 4 a and 4 b illustrate a planform view of a shorter, thick,elliptical planform fin that may be used on shorter surf boards and onsurfboards with multiple fin arrangements. This style of fin can bemanufactured with different tangs to be compatible with different finmounting systems that are commonly found on water sports boards, such asthe Fin Control System™ (FCS) fin plugs of FIG. 4 a, and the Future™ finbox of FIG. 4 b.

FIG. 5 illustrates a thick, elliptical planform fin 10 installed into alongboard 28. The underneath side 28 a of surfboard 28 extends from thenose 28 b to the tail 28 c. A 10.5 inch fin receiver box 22 is mountedin the board, towards the rear of the board, into which the center fin10 from FIG. 3 is installed. Smaller fins 10′ as depicted in FIGS. 4 aand 4 b, commonly called side biters, are installed into receiversforward of center fin 10, close to either edge of the surfboard. Centerfin 10 stands perpendicular to underside 28 a of the surfboard on thecenterline 28 d. The side biter fins 10′ are turned in slightly suchthat they each fall on a corresponding line 28 e of a pair of such linesconverging to a vertex at nose 28 b. The side biter fins are typicallynot perpendicular to the underside of the surfboard but canted away fromthe center of the board by a few degrees.

For these fins, an elliptical area distribution is used. Referring toFIG. 3, the overall height 24 is measured perpendicularly from the planeof root 18 to tip 16. The chord length, measured from leading edge 12 totrailing edge 14 parallel to the fin root (i.e. parallel to thedirection of the flow of water past the fin), at any fin height, can becalculated using the mathematical equations of an ellipse. The fin canbe angled backward or forward at a constant linear slope, or sweptbackward or forward with an elliptical contribution to that slope, orsome combination of both.

FIGS. 6 a-6 d illustrate some examples of various elliptical planformprojections showing the effect of different amounts of constant slopeand elliptical sweep. Regardless of how much the fin is sloped or sweptbackward or forward, the length of the foil chord at a given heightalong the overall height or length 24 would be the same for all finswith the same root chord length and height dimensions. The intent is topreserve the elliptical area distribution and to ensure that the chordlength, and subsequently the foil thickness, decreases from root 18toward tip 16. All of the fins pictured in FIGS. 6 a-6 d have the sameroot chord length and fin height, and as such have the same planformsurface area. The differences between the fins lie in the amount ofconstant linear slope or elliptical sweep.

Fins are designed using the desired characteristics of the fin (finheight, fin root length, constant and elliptical slope parameters, fincant, fin thickness in percentage, and style of fin base). Acorresponding surface map of the desired fin is then generated.Corresponding CNC machine computer code provides for automated machiningof the fins. By changing these various input parameters, the fin can betailored for a specific fin application or for the preferences of itsintended user. For example, moving the center of pressure of the finforward relative to the receiver box makes for a “looser”, that is, moremaneuverable board; the fin acting more like a heel and less like arudder. This may be accomplished using forward slope and/or sweepcomponents to adjust the trajectory of the 30 percent chord line whendesigning the fin.

When designing a fin, its intended surfboard and use are initially takeninto mind. Some determination of the desired size and planform area ofthe fin needs to be made. Surfboards with thruster setups typically havethree identically sized fins. Twin fin setups have two fins that arelarger than the fins for thruster setups. Longboards with 2+1 setupstypically have one larger center fin, and two smaller “side bitter”fins. These side biter fins are smaller than fins for thruster setups.Larger/heavier surfers typically use bigger fins. Bigger surfboardstypically have bigger fins. Larger fins, enable the surfer to pump theboard to build more speed (referred to as drive), but may reduce themaneuverability of the surfboard in certain conditions. Larger fins workbetter on bigger waves, when the surfboard is traveling faster and therider can move rearward on the board with more of his weight over thefins. On smaller waves, smaller fins work better to loosen up thesurfboard and make it more maneuverable when the rider tends to be moreforward on the surfboard, so the board rides flatter in the water. Thetotal area of all the fins on the board, and the placement of those finson the board (forward or rearward on the surfboard), determine a numberof characteristics about the board, including its stability andmaneuverability.

Based on the equation of an ellipse, the height of the fin and thelength of the base or root of the fin determine the area. The semi majoraxis is the height 24 of the fin (variable A in the following equation),the semi minor axis is half the length of the base or root 18 of the fin(variable B in the following equation). The area of an ellipse is givenby the equation, Area=(3.14) A*B. The area of the fin is half the areaof the complete ellipse.

Once the determination of the fin size has been made, specifically theheight of the fin and length of the base, the parameters can be chosento control the projection of the fin as determined by the trajectory ofthe 30 percent chord line. The fin depicted in FIG. 7 stands 8.5 inchestall, and has a base length of 4 inches. 30 percent chord line 32 is theprojection of the 30 percent point, or the thickest portion of the fin.This fin is half of a standard ellipse as it has not been sloped orswept.

The fin can be sloped forward, or rearward with a constant linearcontribution to its slope as illustrated graphically in FIG. 8. Thiscord slope is applied to the 30 percent chord line 32 or the thickestportion of the fin. The leading and trailing edges of the fin adjustaccordingly to maintain the desired planform area.

The fin can be swept forward or rearward with an elliptical contributionto its slope as illustrated graphically in FIG. 9. This sweep is appliedto the 30 percent chord line 32 or the thickest portion of the fin. Theleading and trailing edges of the fin again adjust accordingly tomaintain the desired (constant in FIGS. 6 a-6 d) planform area. FIG. 9shows in particular a rearward elliptical component to sweep, i.e. thefin curves slightly rearward as seen by way of example in FIG. 6 d.

The combination of both the linear and elliptical component of slope andsweep respectively yield the planform projection as seen in FIG. 10.

The combination of linear slope and elliptical sweep offer a widevariety of options for the projection of the planform. The ellipticalcomponent can be used to make the curvature of the fin increaseexponentially along the length of the fin, both forward or rearward. Oneexample as seen in FIGS. 11 a and 11 b is that the elliptical componentof FIG. 11 a can be applied to the 30 percent chord line 32 of FIG. 11b, such that the 30 percent chord line forms a straight line. An exampleof this also seen in FIG. 6 b

The platform profile adjustment by use of the elliptical componentapplied to the 30 percent chord, may be done such that the leading edgeof the fin forms a straight line. In the example of FIGS. 12 a and 12 bthe fin of FIG. 12 b has a rearward linear slope, but a forwardelliptical sweep as a result of the elliptical component adjustments ofFIG. 12 a.

FIG. 12 a as seen in FIGS. 13 a and 13 b, the elliptical components mayalso be applied to the 30 percent chord line 32, such that the trailingedge of the fin forms a straight line.

The combination of linear slope and elliptical sweep offer a great dealof control over the projection or planform of the fin, but do not changethe characteristics of the fin's size or area.

Taking the fin height, fin root length, constant and elliptical slopeand sweep, fin cant, fin thickness in percentage, and style of fin basecharacteristics into account, a variety of fins can be produced fordifferent surfing applications. In all of the fins according to thepresent invention the maximum thickness at the root is substantiallythicker than conventional, and overlaps the opening of the slot 22 a inreceiver box 22, that is broader than the slot 22 a. This is counterintuitive as the fin is usually not wider than the slot in the box sothat the fin will seat properly and fully if the tang is too short forthe box slot receiver depth. That is, conventionally the whole tang andsome of the root will slide into the slot if the slot is too deep untilthe bottom of the tang seats. Different boxes sometimes have differentdepth slots. The boxes 22 are typically ⅜ inch wide (0.375 inch). Slots22 a are typically 0.365 inch wide. The fins of the present inventionmay typically have an average maximum thickness at the root of the ¾inch (0.75 inch) so as to substantially overhang the lip of slot 22 a.Fins 10 may have maximum thickness in the range of ½ inch to one inch.

In addition to forward or rearward slope or sweep, the fin may be cantedto the side when viewed from the front (looking down the chord line fromleading edge to trailing edge). The outermost fins in multi-finarrangements are commonly canted away from the centerline of thesurfboard.

These fins may be manufactured using any combination of method ormaterial that yields the desired shape with sufficient strength toperform their function. Prototype versions of these fins weremanufactured on a computer numerically Controlled (CNC) milling machineout of thick sheets of fiberglass, clear acrylic (commonly calledPlexiglas™), clear polycarbonate (typically used as bullet proof glass),high density polyethylene (HDPE), ultra-high molecular weightpolyethylene (UHMW), and poly vinyl chloride (PVC). Larger scaleproduction methods could employ plastic injection molding, or composite(e.g., fiberglass, carbon fiber, Kevlar™) molding techniques.

As will be apparent to those skilled in the art in the light of theforegoing disclosure, many alterations and modifications are possible inthe practice of this invention without departing from the spirit orscope thereof. Accordingly, the scope of the invention is to beconstrued in accordance with the substance defined by the followingclaims.

1. A surfboard fin for mounting into a slot in a receiver box in theunderside of a surfboard, said fin comprising: an elliptical planformhaving a root and an opposite tip, said root and said tip separated by alongitudinally extending length defining a height of the fin, a leadingedge and an opposite trailing edge extending from said root to said tipalong opposite edge of said planform, said planform having a thicknessdefined by cross-sections of said planform, wherein said cross sectionsare substantially orthogonal to said length, and extend alongcorresponding chords of said cross sections between said opposite edgesso as to extend from said leading edge to said trailing edge, a ratio ofsaid thickness and said chord of each of said cross sections defining acorresponding thickness-to-chord ratio, and wherein substantially all ofsaid thickness-to-chord ratios are substantially equal to one another,and are greater than substantially a thickness-to-chord ratio of twelve,and wherein a ratio of a square of said longitudinally extending lengthand a planform area of said planform define a corresponding aspectratio, and wherein said aspect ratio is less than three, and whereinsaid each of said cross sections has a nose section at a forward endthereof corresponding to said leading edge, a curved mid sectionincluding a maximum thickness position, and a tapered rear sectioncorresponding to said trailing edge, and wherein said nose section, midsection and rear section of said each of said cross sections is definedby a curvature which is substantially that of a non-cambered NACA fourdigit airfoil shape so as to have a substantially parabolic nose sectionand a continuously smoothly substantially convexly curved mid section,where said nose section, said mid section and said rear section form asingle smoothly continuously curved foil section which is symmetric onopposites sides of said chord, and wherein said maximum thicknessposition is located substantially at 30 percent of said chord on saideach of said cross sections, and wherein said length has a linear slopecomponent relative to said root chosen from forward slope, no slope,rearward slope, and wherein said length has an elliptical sweepcomponent relative to said root chosen from forward sweep, no sweep,rearward sweep, and wherein irrespective of said sweep said planform issubstantially elliptical and its corresponding lift distribution is alsosubstantially elliptical and has a surface area which is substantiallyconstant for a particular said aspect ratio and for particular saidcross section and corresponding said thickness-to-chord ratio andcorresponding said maximum thickness position, and wherein said planformdoes not have winglets or auxiliary foils protruding therefrom.
 2. Thefin of claim 1 further comprising a tang depending from said root,wherein a maximum root thickness, defined as said thickness of said rootat said maximum thickness position, is greater than a width of theopening in the slot of the receiver box so as to overhang said root fromthe slot when said tang is mounted in the slot.
 3. The fin of claim 2wherein said maximum root thickness is in the range of substantially onehalf inch to one inch for use with a receiver box having slot width ofless than three eighths of an inch.
 4. The fin of claim 3 wherein saidmaximum root thickness is substantially three quarters of an inch. 5.The fin of claim 1 wherein said linear slope component and saidelliptical sweep component is applied to a substantially 30 percentchord line corresponding to said maximum thickness positions.
 6. The finof claim 5 wherein said slope is forward and said sweep is forward. 7.The fin of claim 5 wherein said slope is forward and said sweep isrearward.
 8. The fin of claim 5 wherein said slope is rearward and saidsweep is forward.
 9. The fin of claim 5 wherein said slope is rearwardand said sweep is rearward.
 10. A method for making a surfboard fin formounting into a slot in a receiver box in the underside of a surfboard,said method comprising the steps of. a) an elliptical planform having aroot and an opposite tip, said root and said tip separated by alongitudinally extending length defining a height of the fin, a leadingedge and an opposite trailing edge extending from said root to said tipalong opposite edge of said planform, said planform having a thicknessdefined by cross-sections of said planform, wherein said cross sectionsare substantially orthogonal to said length, and extend alongcorresponding chords of said cross sections between said opposite edgesso as to extend from said leading edge to said trailing edge, a ratio ofsaid thickness and said chord of each of said cross sections defining acorresponding thickness-to-chord ratio, and wherein substantially all ofsaid thickness-to-chord ratios are substantially equal to one another,and are greater than substantially a thickness-to-chord ratio of twelve,and wherein a ratio of a square of said longitudinally extending lengthand a planform area of said planform define a corresponding aspectratio, and wherein said aspect ratio is less than three, and whereinsaid each of said cross sections has a nose section at a forward endthereof corresponding to said leading edge, a curved mid sectionincluding a maximum thickness position, and a tapered rear sectioncorresponding to said trailing edge, and wherein said nose section, midsection and rear section of said each of said cross sections is definedby a curvature which is substantially that of a non-cambered NACA fourdigit airfoil shape so as to have a substantially parabolic nose sectionand a continuously smoothly substantially convexly curved mid section,where said nose section, said mid section and said rear section form asingle smoothly continuously curved foil section which is symmetric onopposites sides of said chord, and wherein said maximum thicknessposition is located substantially at 30 percent of said chord on saideach of said cross sections, b) choosing length has a linear slopecomponent of said length from forward slope, no slope, rearward slope,and choosing an elliptical sweep component of said length chosen fromforward sweep, no sweep, rearward sweep, c) irrespective of said sweep,maintaining said planform substantially elliptical so that itscorresponding lift distribution is also substantially elliptical andmaintaining a surface area of said planform which is substantiallyconstant for a particular said aspect ratio and for particular saidcross section and corresponding said thickness-to-chord ratio andcorresponding said maximum thickness position.
 11. The method of claim10 further comprising the steps of providing a tang depending from saidroot, and making a maximum root thickness, defined as said thickness ofsaid root at said maximum thickness position, greater than a width ofthe opening in the slot of the receiver box so that said root overhangsfrom the slot when said tang is mounted in the slot.
 12. The method ofclaim 10 wherein said maximum root thickness is chosen from the range ofsubstantially one half inch to one inch for use with a receiver boxhaving a slot width of less than three eighths of an inch.
 13. Themethod of claim 12 wherein said maximum root thickness is substantiallythree quarters of an inch.
 14. The method of claim 10 wherein saidlinear slope component and said elliptical sweep component is applied toa substantially 30 percent chord line corresponding to said maximumthickness positions.
 15. The method of claim 14 wherein said slope isforward and said sweep is forward.
 16. The method of claim 14 whereinsaid slope is forward and said sweep is rearward.
 17. The method ofclaim 14 wherein said slope is rearward and said sweep is forward. 18.The method of claim 14 wherein said slope is rearward and said sweep isrearward.